The Ideal Transformer Equation
- An ideal transformer would be 100% efficient
- Although transformers can increase the voltage of a power source, due to the law of conservation of energy, they cannot increase the power output
- If a transformer is 100% efficient:
Input power = Output power
- The equation to calculate electrical power is:
P = VI
- Where:
- P = power in Watts (W)
- V = potential difference in volts (V)
- I = current in amps (A)
- Therefore, if a transformer is 100% efficient then:
Vp × Ip = Vs × Is
- Where:
- Vp = potential difference across primary coil in volts (V)
- Ip = current through primary coil in Amps (A)
- Vs = potential difference across secondary coil in volts (V)
- Is = current through secondary coil in Amps (A)
- The equation above could also be written as:
Ps = Vp × Ip
- Where:
- Ps = output power (power produced in secondary coil) in Watts (W)
Worked example
A transformer in a travel adapter steps up a 115 V ac mains electricity supply to the 230 V needed for a hair dryer. A current of 5 A flows through the hairdryer.Assuming that the transformer is 100% efficient, calculate the current drawn from the mains supply.
Step 1: List the known quantities
- Voltage in primary coil, Vp = 115 V
- Voltage in secondary coil, Vs = 230 V
- Current in secondary coil, Is = 5 A
Step 2: Write the equation linking the known values to the current drawn from the supply, Ip
Vp × Ip = Vs × Is
Step 3: Substitute in the known values
115 × Ip = 230 × 5
Step 4: Rearrange the equation to find Ip
Step 5: Calculate a value for Ip and include the correct unit
Ip = 10 A
Examiner Tip
Make sure to always check whether the current or potential difference you are substitute is for the correct coil (primary or secondary). If it helps, label these on the question on the exam paper
